<TeXmacs|1.99.4>

<style|<tuple|generic|chinese>>

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  \<#9898\>\<#76EE\>\<#FF1A\>\<#5982\>\<#56FE\>\<#FF0C\>\<#5728\>\<#4E09\>\<#89D2\>\<#5F62\><math|A
  B C>\<#4E2D\>\<#FF0C\>\<#70B9\><math|D>\<#662F\>\<#4E09\>\<#89D2\>\<#5F62\>\<#5916\>\<#4E00\>\<#70B9\>\<#FF0C\>\<#70B9\><math|E>\<#5728\><math|A
  C>\<#8FB9\>\<#4E0A\>\<#FF0C\>\<#70B9\><math|F>\<#5728\>\<#7EBF\>\<#6BB5\><math|C
  D>\<#4E0A\>\<#FF0C\>\<#4E14\><math|A E:A C=C F:C
  D>\<#FF0C\>\<#9762\>\<#79EF\>\<#6BD4\><math|S<rsub|\<triangle\>A B
  D>:S<rsub|\<triangle\>B C D>:S<rsub|\<triangle\>A B
  C>=3:4:1>\<#FF0C\>\<#6C42\>\<#8BC1\>: <math|E F=<frac|1|2>A D>.

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|png>|200px|187px||>>

  \<#8BC1\>\<#660E\>\<#FF1A\> \<#5982\>\<#56FE\>\<#FF0C\>\<#8BBE\>\<#76F4\>\<#7EBF\><math|C
  B>\<#4E0E\>\<#76F4\>\<#7EBF\><math|D A>\<#76F8\>\<#4EA4\>\<#4E8E\>\<#70B9\><math|P>\<#FF0C\>\<#76F4\>\<#7EBF\><math|D
  C>\<#4E0E\>\<#76F4\>\<#7EBF\><math|A B>\<#76F8\>\<#4EA4\>\<#4E8E\>\<#70B9\><math|Q>\<#FF0C\>\<#90A3\>\<#4E48\>\<#6709\>

  <\equation*>
    <frac|S<rsub|\<triangle\>A B D>|S<rsub|\<triangle\>A B C>>=<frac|D Q|C
    Q>=3,<frac|S<rsub|\<triangle\>B C D>|S<rsub|\<triangle\>A B C>>=<frac|D
    P|A P>=4,<frac|S<rsub|\<triangle\>A B D>|S<rsub|\<triangle\>B C
    D>>=<frac|A G|G C>=<frac|3|4>
  </equation*>

  \<#5BF9\><math|\<triangle\>P C D>\<#548C\>\<#622A\>\<#7EBF\><math|A B
  Q>\<#4F7F\>\<#7528\>\<#6885\>\<#6D85\>\<#52B3\>\<#65AF\>\<#5B9A\>\<#7406\>\<#5F97\>

  <\equation*>
    <frac|D A|A P>\<cdot\><frac|P B|B C>\<cdot\><frac|C Q|Q D>=1
  </equation*>

  \<#4E8E\>\<#662F\>\<#6C42\>\<#5F97\><math|<frac|P B|B
  C>=1>\<#FF0C\>\<#518D\>\<#5BF9\><math|\<triangle\>P B
  D>\<#548C\>\<#622A\>\<#7EBF\><math|A G C>\<#4F7F\>\<#7528\>\<#6885\>\<#6D85\>\<#52B3\>\<#65AF\>\<#5B9A\>\<#7406\>\<#5F97\>

  <\equation*>
    <frac|B G|G D>\<cdot\><frac|D A|A P>\<cdot\><frac|P C|C B>=1
  </equation*>

  \<#6C42\>\<#5F97\><math|<frac|B G|G D>=<frac|1|6>>\<#FF0C\>\<#518D\>\<#5BF9\><math|\<triangle\>C
  D G>\<#548C\>\<#622A\>\<#7EBF\><math|B E
  F>\<#4F7F\>\<#7528\>\<#6885\>\<#6C0F\>\<#5B9A\>\<#7406\>\<#5F97\>

  <\equation*>
    <frac|D F|F C>\<cdot\><frac|C E|E G>\<cdot\><frac|G B|B D>=1
  </equation*>

  \<#6211\>\<#4EEC\>\<#5C06\>\<#5229\>\<#7528\>\<#8FD9\>\<#4E2A\>\<#7B49\>\<#5F0F\>\<#6765\>\<#5EFA\>\<#7ACB\>\<#65B9\>\<#7A0B\>\<#FF0C\>\<#7531\>\<#6761\>\<#4EF6\>\<#77E5\><math|<frac|D
  F|F C>=<frac|C E|E A>=\<lambda\>>\<#FF0C\>\<#5219\><math|<frac|C E|E
  G>=<frac|7\<lambda\>|7-3<around*|(|1+\<lambda\>|)>>=<frac|7\<lambda\>|4-3\<lambda\>>>\<#FF0C\>\<#4E8E\>\<#662F\>\<#5F97\>\<#65B9\>\<#7A0B\>

  <\equation*>
    \<lambda\><frac|7\<lambda\>|4-3\<lambda\>>\<cdot\><frac|1|7>=1
  </equation*>

  \<#89E3\>\<#5F97\><math|\<lambda\>=1>\<#FF0C\>\<#6240\>\<#4EE5\><math|F>\<#548C\><math|E>\<#5206\>\<#522B\>\<#662F\><math|C
  D>\<#548C\><math|A C>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\>\<#6240\>\<#4EE5\><math|E
  F=<frac|1|2>A D>.

  \;

  \;
</body>